Identifying multiple periodicities in sparse photon event time series

Abstract

The data considered are event times (e.g. photon arrival times, or the occurrence of sharp pulses). The source is multiperiodic, or the data could be multiperiodic because several unresolved sources contribute to the time series. Most events may be unobserved, either because the source is intermittent, or because some events are below the detection limit. The data may also be contaminated by spurious pulses. The problem considered is the determination of the periods in the data. A two-step procedure is proposed: in the first, a likely period is identified; in the second, events associated with this periodicity are removed from the time series. The steps are repeated until the remaining events do not exhibit any periodicity. A number of period-finding methods from the literature are reviewed, and a new maximum likelihood statistic is also introduced. It is shown that the latter is competitive compared to other techniques. The proposed methodology is tested on simulated data. Observations of two rotating radio transients are discussed, but contrary to claims in the literature, no evidence for multiperiodicity could be found.